Problem: Simplify the following expression: $q = \dfrac{9z}{5} - \dfrac{z}{3}$
In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5$ and $3$ $\lcm(5, 3) = 15$ $ q = \dfrac{3}{3} \cdot \dfrac{9z}{5} - \dfrac{5}{5} \cdot \dfrac{z}{3} $ $q = \dfrac{27z}{15} - \dfrac{5z}{15}$ $q = \dfrac{27z -5z}{15}$ $q = \dfrac{22z}{15}$